Problem: Simplify the following expression: $\dfrac{5z^5}{12z^5}$ You can assume $z \neq 0$.
Answer: $ \dfrac{5z^5}{12z^5} = \dfrac{5}{12} \cdot \dfrac{z^5}{z^5} $ To simplify $\frac{5}{12}$ , find the greatest common factor (GCD) of $5$ and $12$ $5 = 5$ $12 = 2 \cdot 2 \cdot 3$ $ \mbox{GCD}(5, 12) = = 1 $ $ \dfrac{5}{12} \cdot \dfrac{z^5}{z^5} = \dfrac{1 \cdot 5}{1 \cdot 12} \cdot \dfrac{z^5}{z^5} $ $\phantom{ \dfrac{5}{12} \cdot \dfrac{5}{5}} = \dfrac{5}{12} \cdot \dfrac{z^5}{z^5} $ $ \dfrac{z^5}{z^5} = \dfrac{z \cdot z \cdot z \cdot z \cdot z}{z \cdot z \cdot z \cdot z \cdot z} = 1 $ $ \dfrac{5}{12} \cdot 1 = \dfrac{5}{12} $